Auto-weighted Bayesian Physics-Informed Neural Networks and robust estimations for multitask inverse problems in pore-scale imaging of dissolution

• Published in: Computational geosciences Vol. 28; no. 6; pp. 1175 - 1215
• Main Authors: Perez, Sarah, Poncet, Philippe
• Format: Journal Article
• Language: English
• Published: Cham Springer International Publishing 01.12.2024; Springer Nature B.V; Springer Verlag
• Subjects: Bayesian analysis; Bayesian theory; Calcite; Calcite dissolution; Carbon capture and storage; Carbon sequestration; Data assimilation; Data collection; Differential equations; Dimensionless numbers; Dissolution; Dissolving; Earth and Environmental Science; Earth Sciences; Engineering Sciences; Fluid mechanics; Geotechnical Engineering & Applied Earth Sciences; Hydrogeology; Imaging techniques; Inverse problems; Mathematical Modeling and Industrial Mathematics; Mathematical models; Mathematics; Mechanics; Modelling; Multitasking; Neural networks; Numerical Analysis; Observational weighting; Operators (mathematics); Original Paper; Parameter estimation; Parameter uncertainty; Parameters; Physics; Porosity; Probability theory; Reactive fluid environment; Robustness; Soil Science & Conservation; Statistical inference; Uncertainty; Workflow; X ray imagery; X ray microtomography; X rays; Bayesian Physics-Informed Neural Networks; Hamiltonian Monte Carlo; Pore-scale porous media; Multi-objective training; Uncertainty quantification; Imaging inverse problem; Artificial intelligence; Uncertainty Quantification; Artificial Intelligence
• ISSN: 1420-0597; 1573-1499
• DOI: 10.1007/s10596-024-10313-x

In this article, we present a novel data assimilation strategy in pore-scale imaging and demonstrate that this makes it possible to robustly address reactive inverse problems incorporating Uncertainty Quantification (UQ). Pore-scale modeling of reactive flow offers a valuable opportunity to investigate the evolution of macro-scale properties subject to dynamic processes in the context of Carbon Capture and Storage (CCS). Yet, they suffer from imaging limitations arising from the associated X-ray microtomography (X-ray μ CT) process, which induces discrepancies in the properties estimates. Assessment of the kinetic parameters also raises challenges, as reactive coefficients are critical parameters that can cover a wide range of values. We account for these two issues and ensure reliable calibration of pore-scale modeling, based on dynamical μ CT images, by integrating uncertainty quantification in the workflow. The present method is based on a multitasking formulation of reactive inverse problems combining data-driven and physics-informed techniques in calcite dissolution. This allows quantifying morphological uncertainties on the porosity field and estimating reactive parameter ranges through prescribed PDE models, with a latent concentration field, and dynamical μ CT observations. The data assimilation strategy relies on sequential reinforcement incorporating successively additional PDE constraints and suitable formulation of the heterogeneous diffusion differential operator leading to enhanced computational efficiency. We provide a robust and unbiased uncertainty quantification by straightforward adaptive weighting of Bayesian Physics-Informed Neural Networks (BPINNs), ensuring reliable micro-porosity changes during geochemical transformations. We demonstrate successful Bayesian Inference in 1D+Time calcite dissolution based on synthetic μ CT images with meaningful posterior distribution on the reactive parameters and dimensionless numbers. We eventually apply this framework to a more realistic 2D+Time data assimilation problem involving heterogeneous porosity levels and synthetic μ CT dynamical observations.